Solve for $x$. Enter the solutions from least to greatest. $(2x-1)(x+4)=0$ $\text{lesser }x = $
Solution: For any two expressions $A$ and $B$ : If $A\cdot B=0$ then either $A=0$ or $B=0$. This is called the zero product property. In our case, $(2x-1)(x+4)=0$. So either $2x-1=0$ or $x+4=0$ : $\begin{aligned} (1)&&2x-1&=0 \\\\ &&2x&=1 \\\\ &&x&=\dfrac12 \end{aligned}$ $\begin{aligned} (2)&&x+4&=0 \\\\ &&x&=-4 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= -4 \\\\ \text{greater } x &= \dfrac12 \end{aligned}$